SOLUTION: A total of 50 juniors and seniors were given a math test. The 35 juniors attained an average score of 80 while the 15 seniors attained an average of 70. What was the average score

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Question 28831: A total of 50 juniors and seniors were given a math test. The 35 juniors attained an average score of 80 while the 15 seniors attained an average of 70. What was the average score for all 50 students who took the test?
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
these are formulas for averages
(total of juniors scores) / 35 = 80
(total of seniors scores) / 15 = 70
cross-multiply each equation
[1] total of juniors scores = 35*80
[2] total of seniors scores = 15*70
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this is the formula for the whole group average
(total of scores for both juniors and seniors) / 50 = average score
substituting [1] & [2] from above
average score = (35*80 + 15*70) / 50
divide top & bottom by 5
average score = (7*80 + 3*70) / 10
divide top & bottom by 10
average score = (7*8 + 3*7) / 1
average score = 56 + 21 = 77
this makes sense, because since more got 80, the average would be
shifted toward them